A Unified Analysis for Assortment Planning with Marginal Distributions

In this paper, we study assortment planning under the marginal distribution model (MDM), a semiparametric choice model that only requires information about the marginal noise in the utilities of alternatives and does not assume independence of the noise terms. It is already known in the literature that the multinomial logit (MNL) model belongs to the … Read more

Approximation Algorithms for Indefinite Complex Quadratic Maximization Problems

In this paper we consider the following two types of complex quadratic maximization problems: (i) maximize $z^{\HH} Q z$, subject to $z_k^m=1$, $k=1,…,n$, where $Q$ is a Hermitian matrix with $\tr Q=0$ and $z\in \C^n$ is the decision vector; (ii) maximize $\re y^{\HH}Az$, subject to $y_k^m=1$, $k=1,…,p$, and $z_l^m=1$, $l=1,…,q$, where $A\in \C^{p\times q}$ and … Read more

Complex Quadratic Optimization and Semidefinite Programming

In this paper we study the approximation algorithms for a class of discrete quadratic optimization problems in the Hermitian complex form. A special case of the problem that we study corresponds to the max-3-cut model used in a recent paper of Goemans and Williamson. We first develop a closed-form formula to compute the probability of … Read more